Godzilla, King Kong, Mothra, and Ghidorah all seem to have at least a semblance an ability to strategize.

Gigan, Jet Jaguar, and Mechagodzilla 1 are all as smart as their creators, but that's probably because they are directly controlled by said creators.

SpaceGodzilla and Destoroyah are both extremely cunning.

Sanda and Gaira both seem to be somewhat sapient, as does Toho's Frankenstein.

I guess it really depends on your definition of intelligence.

I guess any kind of intelligent, in a broad sense.

Jet Jaguar can think independently. "His" CPU somehow learned to write instructions on its own.

SpaceGodzilla is arguably human or at least almost human level in intelligence for kidnapping baby Godzilla to lure Godzilla. Godzilla showed the same level of intelligence in the Rulers of Earth comic when he used a nuclear reactor to lure Mothra or Destoroyah (don't remember which) so he and Mothra could fight Destoroyah together.

Zilla Jr. displayed strategy whenever he used his burrowing ability to sneak up on enemies, like when he hid in a hole to lure Cyber-Zilla into a surprise attack. There are also other moments of near-human intelligence like when he somehow knew to rescue humans kept in stasis underwater, which he did by creating a whirlpool that made the coccoons float to the surface.

Interesting, very interesting.

I think SpaceGodzilla is most intelligent since he employs real strategy and seems like a more ellegant monster while still using all out brutal attacks, theres just something ellegant about the way SpaceGodzilla fights that really shows how smart he is. Second is Destoroyah since he is a little dumber than SpaceGodzilla, while still using strategy on occasions, in combat he mainly restorts to a savage and demonic assault tactic that makes him seem like a mindless beast, but he is still very intellegent. Third is Battra since he does use strategy but overall resorts to a brutalist aunslaught tactic to overwelm his enemies, he fights that shows intellegence but is shown to be not as smart a Des or Space G

I say forth is Ghidorah since while appearing to be equal to battra, he does employ strategy but mainly uses his abilities constantly enemies weakness through trial and error making him seem overall dumber than Battra. Fifth and final on my list is Gigan, since he was a bit of a mindless pawn in Final Wars, his Showa incarnation employs a more cutthroat esc persona using his slightly above average intellect to use effective strategies but he is down to fifth due to his brutal cutthroat fighting style making him look about as smart as an idiot with a word and laser blaster.